Multifractal Description Of Heterogeneous Characteristics Of Pore-fracture Structure In Natural Reservoir

Pore-fractures of reservoir are important spaces for natural resource and their microstructure directly affects the resource reserves and production difficulties.Therefore,the accurate description of reservoir pore-fracture structure is of great significance for accurate reserve assessment and efficient resource development.Although fractal theory has been increasingly applied to the characterization of porous media,most natural reservoirs show heterogeneous development characteristics,which makes it insufficient to describe them effectively by traditional single fractal theory.However,the emergence of multifractal theory makes it possible.Therefore,the interpretation of multifractal essentially is the prerequisite for accurate description of reservoir heterogeneity.Based on the theory of fractal topography,it is found that multifractal property is derived from diverse scaling behaviors between two successive scaling objects,but the arrangement is the same or statistically the same at all scales.Therefore,multifractal topography was proposed to unify the definition of fractal behaviors in mono-fractals and multifractals.Then,it explains the physical meaning of singularity index?,a scale-invariant parameter,which represents the power-law relationship between the Effective Scaling Lacunarity and the General Scaling Lacunarity.The General Scaling Lacunarity is the geometric mean of the Effective Scaling Lacunarity.Based on the multifractal topography and the new definition of singularity,it was found that:(1)the expectation of singularity index??1;(2)??=1 means mono-fractal,???1 means multifractal.The multifractal particle-filler model is established based on the study of multifractal topography,and the influence of original complexity and fractal behavior parameters on the heterogeneity of the model is discussed and analyzed.The control mechanism of multifractal over the heterogeneity is analyzed by using the singularity index and the heterogeneous seepage parameters obtained by LBM simulation,which lays a foundation for accurate description of the multifractal heterogeneity.The results show:(1)the original complexity controls the heterogeneity by controlling the distribution of the proportion of pore phase,solid phase and fractal phase.The more uniform the distribution is,the weaker the heterogeneity of the final iterative model is.The more discrete the distribution is,the stronger the heterogeneity of the final model is.(2)The parameters to control the heterogeneity of multi-fractal topography are Scaling Coverage F and Scaling Lacunarity P.In the same original complexity,F is used to control the heterogeneity parameters of the model,by controlling the number of fractal phases.When _fx is determined,the larger the F is,the stronger the heterogeneity of the final iteration result will be,and the smaller the F,the weaker the heterogeneity of the final iteration result.(3)The Scaling Lacunarity P determines the singularity index,and the more disperse the singularity index,the more obvious the heterogeneity.